(x+3)^(8)4ix^(5)+i

(a) Write the conjugates of the following: (i) 3+i (ii) 3-i (iii) -sqrt(5)-sqrt(7)i (iv) -sqrt(5)i (v) (4)/(5) (vi) 49-(i)/(7) (vii) (1-i)/(1+i) (viii) (1+i)^(2) (ix) (2+5i)^(2) (x) (-2-(1)/(3)i)^(3) (b) Find the real number x and y if: (i) (x-iy)(3+5i) is the conjugate of -6-24 i (ii) -3+ix^(2)y and x^(2)+y+4i are congugate of each other.

Find each of the following products: (i) (x + 3) (x - 3) (ii) (2x + 5)(2x - 5) (ii) (8 + x)(8 - x) (iv) (7x + 11y) (7x - 11y) (v) (5x^(2) + (3)/(4) y^(2)) (5x^(2) - (3)/(4) y^(2)) (vi) ((4x)/(5) - (5y)/(3)) ((4x)/(5) + (5y)/(3)) (vii) (x + (1)/(x)) (x - (1)/(x)) (viii) ((1)/(x) + (1)/(y)) ((1)/(x) - (1)/(y)) (ix) (2a + (3)/(b)) (2a - (3)/(b))

Simplify : (i) (5/8)^(-7)×\ (8/5)^(-5) (ii) ((-2)/3)^(-2)×\ (4/5)^(-3)

(ix) (x^(3)-(3)/(x^(2)))^(15)

Draw number lines and locate the following points: (i) (1)/(4),(1)/(2),(3)/(4),(4)/(4) (ii) (1)/(8),(2)/(8),(3)/(8),(5)/(8),(7)/(8) (iii) (2)/(5),(3)/(5),(4)/(5),(8)/(5)

Without expanding the determinant at any stage prove that |{:(-5,3+5i,(3)/(2)-4i),(3-5i,8,4+5i),((3)/(2)+4i,4-5i,9):}| has a purely real value.

Whitout expanding the determinat at any stage prove that |{:(-5,3+5i,(3)/(2)-4i),(3-5i,8,4+5i),((3)/(2)+4i,4-5i,9):}| has a purely real value.

Without expanding the determinant at any stage prove that |{:(-5,3+5i,(3)/(2)-4i),(3-5i,8,4+5i),((3)/(2)+4i,4-5i,9):}| has a purely real value.

Whitout expanding the determinat at any stage prove that |{:(-5,3+5i,(3)/(2)-4i),(3-5i,8,4+5i),((3)/(2)+4i,4-5i,9):}| has a purely real value.

find x andy for which the inequalities hold (x^(4)+2ix)-(3x^(2)+iy)=(3-5i)+(1+2iy)